Theorem velpw

Description: Setvar variable membership in a power class. (Contributed by David A. Wheeler, 8-Dec-2018)

	Ref	Expression
Assertion	velpw	⊢ ( 𝑥 ∈ 𝒫 𝐴 ↔ 𝑥 ⊆ 𝐴 )

Proof

Step	Hyp	Ref	Expression
1		vex	⊢ 𝑥 ∈ V
2	1	elpw	⊢ ( 𝑥 ∈ 𝒫 𝐴 ↔ 𝑥 ⊆ 𝐴 )